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Wheeled PROPs, graph complexes and the master equation
Stockholm University, Faculty of Science, Department of Mathematics. (algebra och geometri)
University of Amsterdam.
Prague Institute for mathematics.
2009 (English)In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 213, no 4, 496-535 p.Article in journal (Refereed) Published
Abstract [en]

We introduce and study wheeled PROPs, an extension of the theory of PROPs which can treat traces and, in particular, solutions to the master equations which involve divergence operators. We construct a dg free wheeled PROP whose representations are in one-to-one correspondence with formal germs of SP-manifolds, key geometric objects in the theory of Batalin–Vilkovisky quantization. We also construct minimal wheeled resolutions of classical operads and as non-trivial extensions of the well-known dg operads and . Finally, we apply the above results to a computation of cohomology of a directed version of Kontsevich’s complex of ribbon graphs.

Place, publisher, year, edition, pages
2009. Vol. 213, no 4, 496-535 p.
Keyword [en]
operads, props, homological algebra, homotopy theory
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-35467DOI: 10.1016/j.jpaa.2008.08.007ISI: 000263393700011OAI: oai:DiVA.org:su-35467DiVA: diva2:287377
Available from: 2010-01-18 Created: 2010-01-18 Last updated: 2017-12-12Bibliographically approved

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